Acoustic transducers generally convert electrical signals to acoustic signals (sound waves) and convert received acoustic waves to electrical signals via inverse and direct piezoelectric effect. There are a number of types of acoustic transducers including acoustic resonators, such as bulk acoustic wave (BAW) resonators and surface acoustic wave (SAW) resonators. BAW resonators, in particular, include thin film bulk acoustic resonators (FBARs), which generally have acoustic stacks formed over a substrate cavity, and solidly mounted resonators (SMRs), which generally have acoustic stacks formed over an acoustic mirror (e.g., a distributed Bragg reflector (DBR)). BAW resonators may be used for electrical filters and voltage transformers, for example, in a wide variety of electronic applications, such as cellular telephones, personal digital assistants (PDAs), electronic gaming devices, laptop computers and other portable communications devices.
A BAW resonator has an acoustic stack comprising a layer of piezoelectric material between two conductive plates (e.g., top and bottom electrodes). In response to electrical excitation, the acoustic stack vibrates and an electric field (E-field) is produced within the BAW resonator, which begins at the top electrode and terminates at the bottom electrode. The E-field distribution is dependent on the frequency of the electrical excitation (and the resonant frequency of the BAW resonator). For example, if the electrical excitation is applied at the resonant frequency of the BAW resonator, the integral of the E-field across the top and bottom electrodes will be approximately zero, and therefore, there will be no significant voltage drop from the top to the bottom electrode. Since there is little or no voltage drop across the top and bottom electrodes, there will be little to no E-field generated outside the piezoelectric layer (i.e., little to no parasitic E-field, discussed below). However, if the electrical excitation is applied near the anti-resonant frequency, the integral of the E-field across the electrodes will be significant, producing a large voltage drop across the top and bottom electrodes, and thus generating a significant E-field outside of the piezoelectric layer (i.e., a significant parasitic E-field), as would be apparent to one skilled in the art.
BAW resonators exhibit an electrical response that is primarily linear. That is, when they are excited by a stimulus comprising one or more tones, the BAW resonators produce an electrical (and a mechanical) response comprising primarily the same set of frequencies at which the stimulus was applied. However, as explained further, below, the BAW resonators also exhibit a weakly nonlinear response comprising a weak generation of tones at harmonic frequencies of the applied tones (harmonic generation) and a weak generation of tones at sums and differences of the harmonic frequencies of the applied tones (intermodulation distortion). A portion of the E-field generated outside an active area of the acoustic stack of the BAW resonator is referred to as parasitic E-field. When the electrical excitation is a single tone, it induces a parasitic E-field which passes through a material of the BAW resonator having a weak electric field non-linearity (“nonlinear material”), such as the substrate (e.g., typically formed of silicon (Si)), an electric response which is typically orders of magnitude weaker than the applied tone, is produced at harmonic frequencies. Notably, the density of the electric lines of force—indicative of the strength of the E-field in the nonlinear material (discussed below)—depends on the frequency and signal power of the tone. Typically, a reduction in the strength of the E-field results in a reduction in this nonlinear electric response. When the electrical excitation is a superposition of two or more tones, each at a different frequency, it induces a superposition of E-field distributions in the nonlinear material in response to each of the tones where the E-fields intermodulate or “mix” with one another producing an electric response, which is typically orders of magnitude weaker than any of the applied tones, at sum and difference frequencies of harmonics of the applied tones (“intermodulation distortion (IMD) frequencies”). Notably, the density of the electric lines of force for each tone—indicative of the strength of the E-fields corresponding to each tone in the nonlinear material (discussed below)—depend on the frequency and the signal power of each of each tone. Typically, a reduction in the strength of the E-field in any of the tones, results in a reduction in this nonlinear electric response.
The aforementioned electric responses produced at the harmonic and intermodulation frequencies are “nonlinear responses” which induce “nonlinear currents” that flow through the nonlinear material and/or along the surface of the nonlinear material (e.g., at an interface of the substrate and the acoustic stack of the BAW resonator) and into the electrical terminals of the BAW resonator large enough to interfere with normal operation of the device incorporating the BAW resonator (“interfering nonlinear currents”). For example, when the BAW resonator is part of a radio frequency (RF) acoustic filter, the parasitic E-field(s) result in unwanted nonlinear currents being generated in the RF acoustic filter. In other words, unwanted harmonics and/or mixing products (from tones at two or more frequencies), such as second and third order harmonics and/or IMDs, may result from parasitic E-fields in the nonlinear material.
As described above, in order to reduce the nonlinear response due to the presence of the electric lines of force, there is a need for acoustic resonators configured to minimize or eliminate E-fields from passing through nonlinear materials within the devices, such that nonlinear responses from the acoustic resonator devices and/or from devices (e.g., acoustic filters) that include such acoustic resonator devices are minimized or eliminated. Also, there is a need for minimizing or eliminating the E-fields from passing through such nonlinear materials without negatively affecting other performance characteristics, such as heat transfer and/or structural integrity, of the acoustic resonators and corresponding devices.